Radial Dispersion Peaks as Geometric Observables in Weak Lensing: KiDS and INSPIRE Data

We present a fully model-independent analysis of weak gravitational lensing data from the KiDS survey, identifying a characteristic physical scale associated with the radial dispersion peak of the shear signal measured around individual galaxies treated as autonomous systems. For each system, the dispersion-peak radius r_peak is defined as the radial distance at which the azimuthally averaged dispersion of background galaxy ellipticities reaches its maximum.Using a random sample of 10,000 KiDS anchors, we find a robust and statistically stable modal value at r_peak ≈ 0.31 Mpc. This scale persists under subsampling, bootstrap resampling, and explicit environmental separation, indicating that it is not driven by mass selection, local overdensity, or clustering.We further perform a direct comparative analysis between the random KiDS anchors and a sample of relic galaxies using an identical measurement pipeline. While both samples share the same background catalog and geometric estimator, their dispersion-peak distributions populate distinct scale regimes. In particular, relic galaxies preferentially occupy extended dispersion-peak states that are rarely accessed by random anchors, even when considering control samples larger by several orders of magnitude.These results indicate that the dispersion-peak radius reflects an intrinsic structural property of individual systems rather than a secondary dependence on redshift or environmental selection. The observed scale emerges directly from the statistical organisation of the weak-lensing signal and provides an empirical benchmark for characterising galaxy-scale structure without invoking parametric halo models, virial boundaries, or dynamical assumptions.